Almost 20 jobs are at risk in The Times Ireland Edition newspaper.
A 30-day consultation process is to be held with staff.
The company is considering a return to selling the international edition in print - effectively ending the print version of The Times Ireland Edition.
A spokeswoman said no final decision has been made.
She said the firm's "ongoing focus" of its Irish news operation is its international digital edition, which is sold in more than 150 countries.
However, a source has said just three jobs are set to be retained in the digital edition of the publication.
The Sunday Times in Ireland is unaffected.
Business columnist with The Times Ireland Edition, Tom McEnaney, said: "They're great journalists and each will land well but we will miss an important editorial voice.
"Plurality of opinion in Ireland took a serious hit today."
My thoughts are with everybody at @thetimesIE. They’re great journalists and each will land well but we will miss an important editorial voice. Plurality of opinion in Ireland took a serious hit today.
— Tom McEnaney (@mcenaneytom) May 21, 2019
Journalist with The Sunday Times, John Mooney, said not enough people would pay to read their work.
My colleagues in @thetimesIE were made redundant today. They broke story after story but not enough people would pay €5 a month to read their work. People think journalism costs nothing. If you want to support journalism, you have to pay for it. (https://t.co/L01mPbt0Jm)
— John Mooney (@JohnMooneyIRL) May 21, 2019
The Times Ireland was launched in September 2015 as a digital-only product, with new subscribers being offered an iPad for signing up.
A print edition went on sale in June 2017, with the title hiring more journalists.
